Repeated measures design
repeated measures design, repeated measures design exampleRepeated measures design uses the same subjects with every branch of research, including the control[1] For instance, repeated measurements are collected in a longitudinal study in which change over time is assessed Other nonrepeated measures studies compare the same measure under two or more different conditions For instance, to test the effects of caffeine on cognitive function, a subject's math ability might be tested once after they consume caffeine and another time when they consume a placebo
Contents
 1 Crossover studies
 2 Uses
 3 Order effects
 4 Counterbalancing
 5 Limitations
 6 Repeated measures ANOVA
 61 Partitioning of error
 62 Assumptions
 63 F test
 64 Effect size
 65 Cautions
 7 See also
 8 Notes
 9 References
 91 Design and analysis of experiments
 92 Exploration of longitudinal data
 10 External links
Crossover studies
Main article: Crossover studyA popular repeatedmeasures is the crossover study A crossover study is a longitudinal study in which subjects receive a sequence of different treatments or exposures While crossover studies can be observational studies, many important crossover studies are controlled experiments Crossover designs are common for experiments in many scientific disciplines, for example psychology, education, pharmaceutical science, and healthcare, especially medicine
Randomized, controlled, crossover experiments are especially important in health care In a randomized clinical trial, the subjects are randomly assigned treatments When such a trial is a repeated measures design, the subjects are randomly assigned to a sequence of treatments A crossover clinical trial is a repeatedmeasures design in which each patient is randomly assigned to a sequence of treatments, including at least two treatments of which one may be a standard treatment or a placebo: Thus each patient crosses over from one treatment to another
Nearly all crossover designs have "balance", which means that all subjects should receive the same number of treatments and that all subjects participate for the same number of periods In most crossover trials, each subject receives all treatments
However, many repeatedmeasures designs are not crossovers: the longitudinal study of the sequential effects of repeated treatments need not use any "crossover", for example Vonesh & Chinchilli; Jones & Kenward
Uses
 Limited number of participants —The repeated measure design reduces the variance of estimates of treatmenteffects, allowing statistical inference to be made with fewer subjects[2]
 Efficiency—Repeated measure designs allow many experiments to be completed more quickly, as fewer groups need to be trained to complete an entire experiment For example, experiments in which each condition takes only a few minutes, whereas the training to complete the tasks take as much, if not more time
 Longitudinal analysis—Repeated measure designs allow researchers to monitor how participants change over time, both long and shortterm situations
Order effects
Order effects may occur when a participant in an experiment is able to perform a task and then perform it again Examples of order effects include performance improvement or decline in performance, which may be due to learning effects, boredom or fatigue The impact of order effects may be smaller in longterm longitudinal studies or by counterbalancing using a crossover design
Counterbalancing
In this technique, two groups each perform the same tasks or experience the same conditions, but in reverse order With two tasks or conditions, four groups are formed
Counter BalancingTask/Condition  Task/Condition  Remarks  

Group A  1  2  Group A performs Task/Condition 1 first, then Task/Condition 2 
Group B  2  1  Group B performs Task/Condition 2 first, then Task/Condition 1 
Counterbalancing attempts to take account of two important sources of systematic variation in this type of design: practice and boredom effects Both might otherwise lead to different performance of participants due to familiarity with or tiredness to the treatments
Limitations
It may not be possible for each participant to be in all conditions of the experiment ie time constraints, location of experiment, etc Severely diseased subjects tend to drop out of longitudinal studies, potentially biasing the results In these cases mixed effects models would be preferable as they can deal with missing values
Mean regression may affect conditions with significant repetitions Maturation may affect studies that extend over time Events outside the experiment may change the response between repetitions
Repeated measures ANOVA
Repeated measures analysis of variance rANOVA is a commonly used statistical approach to repeated measure designs[3] With such designs, the repeatedmeasure factor the qualitative independent variable is the withinsubjects factor, while the dependent quantitative variable on which each participant is measured is the dependent variable
Partitioning of error
One of the greatest advantages to rANOVA, as is the case with repeated measures designs in general, is the ability to partition out variability due to individual differences Consider the general structure of the Fstatistic:
F = MSTreatment / MSError = SSTreatment/dfTreatment/SSError/dfError
In a betweensubjects design there is an element of variance due to individual difference that is combined with the treatment and error terms:
SSTotal = SSTreatment + SSError
dfTotal = n1
In a repeated measures design it is possible to partition subject variability from the treatment and error terms In such a case, variability can be broken down into betweentreatments variability or withinsubjects effects, excluding individual differences and withintreatments variability The withintreatments variability can be further partitioned into betweensubjects variability individual differences and error excluding the individual differences:[4]
SSTotal = SSTreatment excluding individual difference + SSSubjects + SSError
dfTotal = dfTreatment within subjects + dfbetween subjects + dferror = k1 + n1 + nkn1
In reference to the general structure of the Fstatistic, it is clear that by partitioning out the betweensubjects variability, the Fvalue will increase because the sum of squares error term will be smaller resulting in a smaller MSError It is noteworthy that partitioning variability reduces degrees of freedom from the Ftest, therefore the betweensubjects variability must be significant enough to offset the loss in degrees of freedom If betweensubjects variability is small this process may actually reduce the Fvalue[4]
Assumptions
As with all statistical analyses, specific assumptions should be met to justify the use of this test Violations can moderately to severely affect results and often lead to an inflation of type 1 error With the rANOVA, standard univariate and multivariate assumptions apply[5] The univariate assumptions are:
 Normality—For each level of the withinsubjects factor, the dependent variable must have a normal distribution
 Sphericity—Difference scores computed between two levels of a withinsubjects factor must have the same variance for the comparison of any two levels This assumption only applies if there are more than 2 levels of the independent variable
 Randomness—Cases should be derived from a random sample, and scores from different participants should be independent of each other
The rANOVA also requires that certain multivariate assumptions be met, because a multivariate test is conducted on difference scores These assumptions include:
 Multivariate normality—The difference scores are multivariately normally distributed in the population
 Randomness—Individual cases should be derived from a random sample, and the difference scores for each participant are independent from those of another participant
F test
As with other analysis of variance tests, the rANOVA makes use of an F statistic to determine significance Depending on the number of withinsubjects factors and assumption violations, it is necessary to select the most appropriate of three tests:[5]
 Standard Univariate ANOVA F test—This test is commonly used given only two levels of the withinsubjects factor ie time point 1 and time point 2 This test is not recommended given more than 2 levels of the withinsubjects factor because the assumption of sphericity is commonly violated in such cases
 Alternative Univariate test[6]—These tests account for violations to the assumption of sphericity, and can be used when the withinsubjects factor exceeds 2 levels The F statistic is the same as in the Standard Univariate ANOVA F test, but is associated with a more accurate pvalue This correction is done by adjusting the degrees of freedom downward for determining the critical F value Two corrections are commonly used—The GreenhouseGeisser correction and the HuynhFeldt correction The GreenhouseGeisser correction is more conservative, but addresses a common issue of increasing variability over time in a repeatedmeasures design[7] The HuynhFeldt correction is less conservative, but does not address issues of increasing variability It has been suggested that lower HuynhFeldt be used with smaller departures from sphericity, while GreenhouseGeisser be used when the departures are large
 Multivariate Test—This test does not assume sphericity, but is also highly conservative
Effect size
One of the most commonly reported effect size statistics for rANOVA is partial etasquared ηp2 It is also common to use the multivariate η2 when the assumption of sphericity has been violated, and the multivariate test statistic is reported A third effect size statistic that is reported is the generalized η2, which is comparable to ηp2 in a oneway repeated measures ANOVA It has been shown to be a better estimate of effect size with other withinsubjects tests[8][9]
Cautions
rANOVA is not always the best statistical analysis for repeated measure designs The rANOVA is vulnerable to effects from missing values, imputation, unequivalent time points between subjects and violations of sphericity[10] These issues can result in sampling bias and inflated rates of Type I error[11] In such cases it may be better to consider use of a linear mixed model[12]
See also
 Analysis of variance
 Clinical trial protocol
 Crossover study
 Design of experiments
 Glossary of experimental design
 Longitudinal study
 Growth curve
 Missing data
 Mixed models
 Multivariate analysis
 Observational study
 Optimal design
 Panel analysis
 Panel data
 Panel study
 Randomization
 Randomized controlled trial
 Repeated measures design
 Sequence
 Statistical inference
 Treatment effect
Notes
 ^ Shuttleworth, Martyn 20091126 "Repeated Measures Design" Experimentresourcescom Retrieved 20130902
 ^ Barret, Julia R 2013 "Particulate Matter and Cardiovascular Disease: Researchers Turn an Eye toward Microvascular Changes" Environmental Health Perspectives 121: a282 doi:101289/ehp121A282 PMC 3764084 PMID 24004855
 ^ Gueorguieva; Krystal 2004 "Move Over ANOVA" Arch Gen Psychiatry 61: 310 doi:101001/archpsyc613310
 ^ a b Howell, David C 2010 Statistical methods for psychology 7th ed Belmont, CA: Thomson Wadsworth ISBN 9780495597841
 ^ a b Salkind, Samuel B Green, Neil J Using SPSS for Windows and Macintosh : analyzing and understanding data 6th ed Boston: Prentice Hall ISBN 9780205020409
 ^ Vasey; Thayer 1987 "The Continuing Problem of False Positives in Repeated Measures ANOVA in Psychophysiology: A Multivariate Solution" Psychophysiology 24: 479–486 doi:101111/j146989861987tb00324x
 ^ Park 1993 "A comparison of the generalized estimating equation approach with the maximum likelihood approach for repeated measurements" Stat Med 12: 1723–1732 doi:101002/sim4780121807
 ^ Bakeman 2005 "Recommended effect size statistics for repeated measures designs" Behavior Research Methods 37 3: 379–384 doi:103758/bf03192707
 ^ Olejnik; Algina 2003 "Generalized eta and omega squared statistics: Measures of effect size for some common research designs" Psychological Methods 8: 434–447 doi:101037/1082989x84434
 ^ Gueorguieva; Krystal 2004 "Move Over ANOVA" Arch Gen Psychiatry 61: 310–317 doi:101001/archpsyc613310
 ^ Muller; Barton 1989 "Approximate Power for Repeated Measures ANOVA lacking sphericity" Journal of the American Statistical Association 84 406: 549–555 doi:101080/01621459198910478802
 ^ Kreuger; Tian 2004 "A comparison of the general linear mixed model and repeated measures ANOVA using a dataset with multiple missing data points" Biological Research for Nursing 6: 151–157 doi:101177/1099800404267682
References
Design and analysis of experiments
 Jones, Byron; Kenward, Michael G 2003 Design and Analysis of CrossOver Trials Second ed London: Chapman and Hall
 Vonesh, Edward F & Chinchilli, Vernon G 1997 Linear and Nonlinear Models for the Analysis of Repeated Measurements London: Chapman and Hall
Exploration of longitudinal data
 Davidian, Marie; David M Giltinan 1995 Nonlinear Models for Repeated Measurement Data Chapman & Hall/CRC Monographs on Statistics & Applied Probability ISBN 9780412983412
 Fitzmaurice, Garrett, Davidian, Marie, Verbeke, Geert and Molenberghs, Geert, eds 2008 Longitudinal Data Analysis Boca Raton, Florida: Chapman and Hall/CRC ISBN 1584886587 CS1 maint: Uses editors parameter link
 Jones, Byron; Kenward, Michael G 2003 Design and Analysis of CrossOver Trials Second ed London: Chapman and Hall
 Kim, Kevin & Timm, Neil 2007 ""Restricted MGLM and growth curve model" Chapter 7" Univariate and multivariate general linear models: Theory and applications with SAS with 1 CDROM for Windows and UNIX Statistics: Textbooks and Monographs Second ed Boca Raton, Florida: Chapman & Hall/CRC ISBN 9781584886341
 Kollo, Tõnu & von Rosen, Dietrich 2005 ""Multivariate linear models" chapter 4, especially "The Growth curve model and extensions" Chapter 41" Advanced multivariate statistics with matrices Mathematics and its applications 579 New York: Springer ISBN 9781402034183
 Kshirsagar, Anant M & Smith, William Boyce 1995 Growth curves Statistics: Textbooks and Monographs 145 New York: Marcel Dekker, Inc ISBN 0824793412
 Pan, JianXin & Fang, KaiTai 2002 Growth curve models and statistical diagnostics Springer Series in Statistics New York: SpringerVerlag ISBN 0387950532
 Seber, G A F & Wild, C J 1989 ""Growth models Chapter 7"" Nonlinear regression Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics New York: John Wiley & Sons, Inc pp 325–367 ISBN 0471617601
 Timm, Neil H 2002 ""The general MANOVA model GMANOVA" Chapter 36d" Applied multivariate analysis Springer Texts in Statistics New York: SpringerVerlag ISBN 0387953477
 Vonesh, Edward F & Chinchilli, Vernon G 1997 Linear and Nonlinear Models for the Analysis of Repeated Measurements London: Chapman and Hall Comprehensive treatment of theory and practice
 Conaway, M 1999, October 11 Repeated Measures Design Retrieved February 18, 2008, from http://biostatmcvanderbiltedu/twiki/pub/Main/ClinStat/repmeasPDF
 Minke, A 1997, January Conducting Repeated Measures Analyses: Experimental Design Considerations Retrieved February 18, 2008, from Ericaenet: http://ericaenet/ft/tamu/Rmhtm
 Shaughnessy, J J 2006 Research Methods in Psychology New York: McGrawHill
External links
 Examples of all ANOVA and ANCOVA models with up to three treatment factors, including randomized block, split plot, repeated measures, and Latin squares, and their analysis in R University of Southampton
 

Scientific method 

Treatment and blocking 

Models and inference 

Designs Completely randomized 


 

 
 
 
 
 
 
 

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Repeated measures design
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